IS

the principles op bridges.

TRACT I.

being connected together by joints at their extremities, andfreely moveable about them, maybe placed in such a verticalposition, as to be exactly balanced, or kept in equilibrio, bytheir mutual thrusts and pressures at the joints ; and that theeffect will be the same if the bars themselves be considered aswithout weight, and the angles be pressed down by laying onthem weights which shall be equal to the vertical pressuresat the same angles, produced by the bars in the case whenthey are considered as endued with their own natural weights.And as we have found that the bars may be of any length,without affecting the general properties and proportions ofthe thrusts and pressures, therefore by supposing them to be-come short, like arch stones, it is plain that we shall thenhave the same principles and properties accommodated to areal arch of equilibration, or one that supports itself in a per-fect balance. It may be further observed, that the conclu-sions here derived, in this proposition and its corollaries,exactly agree with those derived in a very different way, inthe former editions of the principles of bridges, viz, in props.J and 2, and their corollaries and which have been here re-peated, in the foregoing prop. 2.

PROP. IV.

If the whole figure in the third proposition he inverted, orturned round the horizontal line ag as an axis, till it Ik com-pletely reversed, or in the same vertical plane below the firstposition, each angle d, d, He, being in the same plumb line ;and if weights i, k, l, m, n, which are respectively equal to theweights laid on the angles b, c, d, k, f, of the first figure, benow suspended by threads from the corresponding angles b,e, d,c, f, of the lower figure ; then will those weights keep this figurein exact equilibria, the same as the former , and all the tensionsor forces in the latter case, whether vertical or horizontalor oblique, will be exactly equal to the corresponding forcesof weight or pressure or thrust in the like directions of thefirst figure.